PRP Records

Probable Primes Top 10000

(172142 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
80013^114869+7654807Lelio R Paula10/2012
80028^60681-60681^854801Norbert Schneider12/2016
80031897^16710+16710^189754777Serge Batalov05/2014
8004Phi(61868,59)54776Enzo Doria04/2012
8005113^26679+254775Lelio R Paula05/2013
80063^114789-7454769Lelio R Paula10/2012
800715^46567+9854768Lelio R Paula02/2013
8008(2*10^54767-71)/354767Robert Price01/2017
8009(21*2^181931-1)/16999754763Lelio R Paula01/2014
80102^181913+2954762Henri Lifchitz06/2005
8011(31*10^54761-121)/954762Robert Price06/2016
80122^181887+18954754Lelio R Paula02/2011
80132^181874+181874^2-154750Robert Price04/2014
8014(2^181865+9)/733954743Lelio R Paula02/2012
80155^78314-9254740Lelio R Paula10/2012
8016(163*10^54727-1)/954729Serge Batalov12/2014
801715^46531+7454725Lelio R Paula02/2013
8018277^22400-34854712Enzo Doria07/2012
80196^70302+10154706Lelio R Paula10/2012
80203^114622-1040854689Enzo Doria02/2013
8022(23*2^181674+1)/48954688Lelio R Paula01/2012
80212^181669-155154688Yves Minet08/2012
8023(57352^11491-1)/5735154676Serge Batalov04/2015
8024(31*2^181629-1)/1073472154671Lelio R Paula01/2014
8025(F(1048)^251-F(1047)^251)/F(1046)54668Wayne Halsdorf05/2010
802613^49073+4654665Lelio R Paula01/2013
8027(57042^11491-1)/5704154649Serge Batalov04/2015
802920^42000+7354644Lelio R Paula02/2013
8028(67607*2^181517+1)/165554644Lelio R Paula05/2014
803033*10^54634+754636Robert Price07/2016
803120^41988+6154628Lelio R Paula01/2013
803220^41988-812354628Enzo Doria03/2013
80332^181420+2118154613Yves Minet03/2011
8034(19*10^54608+161)/954609Robert Price07/2016
803519^42696-2454598Lelio R Paula02/2013
8036(74*10^54583+61)/954584Robert Price10/2015
80372^181316-9439554582Lelio R Paula09/2011
803814751^5006+5006^1475154572Hans Havermann08/2016
803914^47609+3954567Lelio R Paula02/2013
80403^114327-7454548Lelio R Paula10/2012
8041gcd(V(995625),5*F(199125)*(F(199125)-1)+1)54546Serge Batalov04/2015
80422^181155-1155*18115554534Henri Lifchitz02/2005
8043Phi(61672,83)54533Enzo Doria05/2012
80449*2^181128+754526Lelio R Paula03/2014
804589*10^54518-754520Robert Price03/2017
80462^181090-11324754514Enzo Doria07/2014
804714031^7670+7670^1403154508Hans Havermann08/2016
804814210^6849+6849^1421054505Hans Havermann08/2016
80492^181043-19954500Lelio R Paula02/2011
805012^50499+554498Lelio R Paula01/2013
805112^50491+554489Lelio R Paula01/2013
80526^70016-14554484Lelio R Paula10/2012
805311^52313-960054479Enzo Doria02/2013
80542^64459+3^64459+5^64459+7^6445954475Henri Lifchitz08/2001
80552^180946-11104154471Enzo Doria05/2014
8056(64*10^54467+287)/954468Robert Price04/2016
80575^77907-2*3^7790754455Mike Oakes11/2009
805820^41853-562354453Enzo Doria03/2013
805914^47506-7554448Lelio R Paula02/2013
80602^180839-11343754438Enzo Doria08/2014
80613^114085+2854433Lelio R Paula10/2012
8062Phi(141230,10)54432Ray Chandler08/2009
80636^69946-5554429Lelio R Paula10/2012
80645*2^180796+354426Lelio R Paula03/2014
8065(23*2^180782-1)/9154421Lelio R Paula01/2014
80669*6^69928-754416Lelio R Paula09/2014
806792^27701-91^2770154399Robert Price08/2015
8068(2^180687-3)*6-754393Gilbert Mozzo04/2016
8069(5*10^54388-11)/354389Erik Branger12/2013
807020^41799-304354382Enzo Doria03/2013
807113860^8387+8387^1386054382Hans Havermann08/2016
8072(F(19)^15017-F(18)^15017)/F(17)54378Wayne Halsdorf05/2010
80737^64329-1854365Lelio R Paula10/2012
80742^180551-96754352Yves Minet01/2012
807515^46209-7454347Lelio R Paula02/2013
807610^54345+2973954346Patrick De Geest08/2013
807710^54345-14138154345Patrick De Geest09/2013
8078lucasU(2098,1,16360)-lucasU(2098,1,16359)54342Mike Oakes05/2009
80792^180496+1554335Lelio R Paula02/2011
80801845^16636+16636^184554334Serge Batalov05/2014
808111^52169-7054329Lelio R Paula01/2013
808213693^9262+9262^1369354317Hans Havermann06/2016
80832^180429-11310154315Enzo Doria07/2014
80842^180423-11205154313Enzo Doria05/2014
808516112^2349+2349^1611254312Hans Havermann06/2016
8086(13^48751+4^48751)/1754305Robert Price05/2013
80872^180370+1291554297Lelio R Paula09/2012
8088(10^54290+41)/354290Robert Price01/2017
808915108^3917+3917^1510854283Hans Havermann06/2016
80902^180317-301954281Yves Minet10/2014
80912^180314+85554280Lelio R Paula10/2009
809219^42425+9454252Lelio R Paula02/2013
80932^180180-100544954240Paul Bourdelais11/2012
80942^180173-277354238Yves Minet07/2014
809513367^11418+11418^1336754238Hans Havermann06/2016
8096427^20614+20614^42754224Norbert Schneider06/2016
80972^180124-8795954223Gary Barnes08/2009
80982^180111-11310154219Enzo Doria07/2014
80992^180101-11487154216Enzo Doria05/2015
8100(11*2^180099+1)/5161754212Lelio R Paula07/2012
81022^180070+46554207Lelio R Paula09/2012
810113683^9154+9154^1368354207Hans Havermann06/2016
8103810522513*2^180009-9531*2^9531-154198Jiong Sun12/2003
81042^180014+61354190Jason Earls04/2008
81052^180007+10154188Lelio R Paula02/2011
81062^180001+4187754186Jim Fougeron08/2002
81072^180000+13015354186Jim Fougeron09/2002
81083^113565-7454185Lelio R Paula10/2012
810950^31891-4954182Norbert Schneider07/2014
8110(5*2^179991-1)/1142754180Lelio R Paula01/2014
81113^113548+2654177Lelio R Paula10/2012
81124159^14969-13854173Enzo Doria07/2012
81132^179955+577554172Lelio R Paula10/2009
81142^179953-23131354172Enzo Doria05/2014
81155^77485+654160Lelio R Paula10/2012
811618^43141+8554154Lelio R Paula02/2013
81173^113489-34054149Lelio R Paula10/2012
81187^64070+9054146Lelio R Paula10/2012
811918^43131+7154142Lelio R Paula02/2013
81202^179826-13154134Lelio R Paula02/2011
81212^179815-11273554130Enzo Doria06/2014
81222^179806+7384954127Enzo Doria04/2016
81232^179790+3354123Donovan Johnson02/2006
812414287^6138+6138^1428754120Hans Havermann06/2016
8125(17*10^54117+1)/954118Serge Batalov05/2010
81262^179763-18954115Lelio R Paula02/2011
8127(21181*2^179770+1)/302910554115Lelio R Paula05/2014
81281828^16589+16589^182854113Serge Batalov05/2014
813020^41588-588354108Enzo Doria03/2013
812950^31847-4954108Norbert Schneider07/2014
81312^179733-685554106Lelio R Paula10/2009
813220^41584-558354103Enzo Doria03/2013
813310^54084+3*3^5408454085Mike Oakes05/2010
81342^179613-179554069Lelio R Paula10/2009
81352^179589-101152354062Paul Bourdelais11/2012
81362^179574-253154058Yves Minet07/2014
8137(41*10^54051-23)/954052Robert Price05/2015
8138117^26131-11654044Norbert Schneider10/2013
8139(10^54038-31)/354038Serge Batalov12/2014
814011^51885-8454033Lelio R Paula01/2013
814114990^4011+4011^1499054013Hans Havermann07/2016
8142(19*2^179414+1)/754010Lelio R Paula07/2012
81433^113182-1040854002Enzo Doria02/2013
814435^34970-878653997Enzo Doria03/2013
81452^179371-163758753997Enzo Doria05/2015
814619^42225-9253996Lelio R Paula01/2013
8147(3^113188+7)/7391767578453994Lelio R Paula03/2012
81487*3^113162+853993Lelio R Paula03/2014
8149(10^53991+179)/953991Serge Batalov12/2014
81502^179350-214553990Lelio R Paula10/2009
81518^59782-6^59782-3^5978253989Mike Oakes11/2009
81523*7^63861+853970Lelio R Paula09/2014
81532^179274+7138953967Enzo Doria04/2016
81542^179259-5869553963Lelio R Paula10/2009
81556^69345+6153961Lelio R Paula10/2012
8156(40216^11719-1)/4021553955Serge Batalov04/2015
815714^47067-353945Lelio R Paula01/2013
8158(2^179168-5)/5953934Lelio R Paula02/2012
81592^179128+841553923Lelio R Paula07/2012
81602^179120+253353921Henri Lifchitz09/2004
8161(2^179126+78557)/464932118753913Lelio R Paula05/2012
816374^28842+7353913Norbert Schneider11/2012
81621271^17368+17368^127153913Serge Batalov05/2014
81642^179079+5353909Lelio R Paula02/2011
816517^43807+5453903Lelio R Paula01/2013
816617^43807+3053903Lelio R Paula01/2013
81673^112951-31053892Lelio R Paula10/2012
8168Phi(7,2957!)53888Robert Price05/2015
8169(10223*2^178975+1)/3398553877Lelio R Paula05/2014
81702^178944-21920953868Enzo Doria11/2012
8171(10^53859+149)/353859Serge Batalov12/2014
81722^178910-19153858Lelio R Paula02/2011
817316170^2141+2141^1617053857Hans Havermann07/2016
8174(5*10^53855-107)/353856Robert Price01/2017
8175(72*10^53847-27)/9953847Patrick De Geest08/2004
81762^178841-86968810553837Lelio R Paula06/2012
81772*10^53834-2753835Robert Price02/2017
81782^178821-101152353831Paul Bourdelais11/2012
81792^178819-1553830Lelio R Paula02/2011
8180(14450!-1)/22529658153829Donovan Johnson04/2006
81812^178761-46553813Lelio R Paula10/2009
818218900^703+703^1890053808Anatoly F. Selevich02/2007
818313918^7343+7343^1391853806Hans Havermann08/2016
818410^53804+3174953805Patrick De Geest12/2012
818510^53804-7153804Robert Price05/2011
8186t(178994)53804Robert Price03/2015
8187(2^178693-lucasV(1,2,178693)+1)/253792Mike Oakes11/2016
81882^178671-11321553786Enzo Doria07/2014
818915110^3621+3621^1511053774Hans Havermann07/2016
81902^178611+9553768Lelio R Paula02/2011
81912^178597+571153764Lelio R Paula10/2011
81922^178598+1291553764Lelio R Paula07/2012
8193(9179*2^178579-1)/30353760Lelio R Paula03/2015
81945*7^63589+253740Lelio R Paula09/2014
81952^178516-11251553739Enzo Doria06/2014
819620^41302-2753736Lelio R Paula01/2013
81976^69054-3920953735Mike Oakes12/2010
819813086^12769+12769^1308653734Hans Havermann07/2016
81992^178455+7604353721Enzo Doria04/2016
8200(10^53718-7)/353718Makoto Kamada10/2004
8201(67607*2^178426+1)/353716Lelio R Paula05/2014
82029*10^53707+1153708Robert Kinser01/2017
820313214^11595+11595^1321453706Hans Havermann07/2016
8204Phi(134350,10)/537401/801196225153705Maksym Voznyy10/2011
82052^178367-37953694Yves Minet03/2013
8206(2^178364-5)/1153692Lelio R Paula02/2012
82074339^14760-16853688Enzo Doria06/2012
820812^49746-1153685Lelio R Paula01/2013
8210(9913*2^178266-1)/224753665Lelio R Paula03/2015
820913725^8128+8128^1372553665Hans Havermann07/2016
82112^178250-11326153659Enzo Doria07/2014
82122^178226+1171553652Lelio R Paula10/2009
821335^34742-197653645Enzo Doria03/2013
821420^41228-56353639Enzo Doria03/2013
8215359^20992+20992^35953637Norbert Schneider08/2014
8216(27*2^178183-1)/2906553636Lelio R Paula01/2014
8217(3^112414+7)/3738169653628Lelio R Paula03/2012
821817994^955+955^1799453623Anatoly F. Selevich10/2006
82192^178117-155153619Yves Minet08/2012
82202^178099-1128753614Enzo Doria06/2014
8221(15*2^178080-1)/30907153604Lelio R Paula01/2014
82225^76672-1376653592Enzo Doria02/2013
82236^68868-13753590Lelio R Paula10/2012
8224(5*2^178021+1)/817353587Lelio R Paula07/2012
82255^76654-2653579Lelio R Paula10/2012
8226(3^112297-2)/762753576Lelio R Paula03/2012
82273*2^177948-753569Lelio R Paula03/2014
822810^53558+1854353559Patrick De Geest12/2012
822910^53558-2153558Robert Price03/2011
82302^177792-9553521Lelio R Paula02/2011
823113392^9919+9919^1339253521Hans Havermann07/2016
823213105^12132+12132^1310553520Hans Havermann07/2016
823313^48042+8253517Lelio R Paula01/2013
82342^177768+3912153514Yves Minet10/2010
823513835^7366+7366^1383553504Hans Havermann07/2016
823617^43477+8453497Lelio R Paula01/2013
82375*10^53492+953493Dmitry Domanov11/2010
82382^177683+9553488Lelio R Paula01/2011
8239(2^177678+3)/51462753481Lelio R Paula02/2012
82402^177641-25546353476Gary Barnes08/2009
8241p(11608)#/2+1653469Robert Price12/2016
824237302#*10^(37302+52)+p(37302+1)53457Jason Earls08/2008
82431829^16384+1828^1638453449Henri Lifchitz01/2007
824435^34608-960253438Enzo Doria03/2013
8245(3^111992+8)/1486753430Lelio R Paula03/2012
82462^177480+186966153427Enzo Doria05/2016
8247(8*10^53411+1)/953411Serge Batalov12/2008
82484*5^76410-353409Lelio R Paula09/2014
82492^177380-11304553397Enzo Doria07/2014
82505^76362-2*3^7636253375Mike Oakes11/2009


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 18 2017 12:02 (Time in France)

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